{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Goal - show examples of cross-validation for model selection and bootstrapping for prediction error estimation.\n",
    "</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from sklearn.metrics import confusion_matrix, roc_auc_score\n",
    "from sklearn import linear_model\n",
    "import course_utils as bd\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "%matplotlib inline\n",
    "reload(bd)\n",
    "\n",
    "#Load data and downsample for a 50/50 split, then split into a train/test\n",
    "f = '/Users/briand/Desktop/ds course/datasets/ads_dataset_cut.txt'\n",
    "\n",
    "train_split = 0.8\n",
    "tdat = pd.read_csv(f, header = 0,sep = '\\t')\n",
    "moddat = bd.downSample(tdat, 'y_buy', 4)\n",
    "\n",
    "#We know the dataset is sorted so we can just split by index\n",
    "train = moddat[:int(np.floor(moddat.shape[0]*train_split))]\n",
    "test = moddat[int(np.floor(moddat.shape[0]*train_split)):]\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Let's say we want to build a classifier that does ranking based on the probability of the label being 1. We can use Logistic Regression with AUC as our validation metric. We need to choose a regularization weight, but because we have limited data, we can do this via cross-validation.<br><br>\n",
    "\n",
    "The following function performs the cross-validation for various levels of C\n",
    "\n",
    "</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from sklearn.cross_validation import *\n",
    "\n",
    "def xValAUC(tr, lab, k, cs):\n",
    "    '''\n",
    "    Perform k-fold cross validation on logistic regression, varies C,\n",
    "    returns a dictionary where key=c,value=[auc-c1, auc-c2, ...auc-ck].\n",
    "    '''\n",
    "    cv = KFold(n = tr.shape[0], n_folds = k)\n",
    "    aucs = {}\n",
    "\n",
    "    for train_index, test_index in cv:\n",
    "        tr_f = tr.iloc[train_index]\n",
    "        va_f = tr.iloc[test_index]\n",
    "    \n",
    "        for c in cs:\n",
    "            logreg = linear_model.LogisticRegression(C = c)\n",
    "            logreg.fit(tr_f.drop(lab, 1),tr_f[lab])\n",
    "            met = roc_auc_score(va_f[lab], logreg.predict_proba(va_f.drop(lab,1))[:,1])\n",
    "\n",
    "            if (aucs.has_key(c)):\n",
    "                aucs[c].append(met)\n",
    "            else:\n",
    "                aucs[c] = [met]\n",
    "    \n",
    "    return aucs\n",
    "\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Now we can run our experiment</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "xval_dict = {'e':[], 'mu':[], 'sig':[]}\n",
    "k = 10\n",
    "auc_cv = xValAUC(train, 'y_buy', k, [10**i for i in range(-20,20)])\n",
    "for i in range(-20,20):\n",
    "    xval_dict['e'].append(i)\n",
    "    xval_dict['mu'].append(np.array(auc_cv[10**i]).mean())\n",
    "    xval_dict['sig'].append(np.sqrt(np.array(auc_cv[10**i]).var()))\n",
    "    \n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>We can now load the results from above into a dataframe and begin to analyze\n",
    "\n",
    "</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "res = pd.DataFrame(xval_dict)\n",
    "\n",
    "#Get the confidence intervals\n",
    "res['low'] = res['mu'] - 1.96*res['sig']/np.sqrt(10)\n",
    "res['up'] = res['mu'] + 1.96*res['sig']/np.sqrt(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Now let's plot the results to get a sense of how AUC varies with regularization strength. We'll also plot the lower and upper 95% confidence bands to get a sense of the variance.\n",
    "</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x109e07550>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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vcQzdUeTL/cB2pT92reCeA7d33XIk0pgyM4RHkoycgVVJtQMbAVOBbbCgsRt2xzHMb58D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\nLml8pv4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10396cb90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111)\n",
    "\n",
    "plt.plot(res['e'], res['mu'])\n",
    "plt.plot(res['e'], res['low'], 'k--')\n",
    "plt.plot(res['e'], res['up'], 'k--')\n",
    "\n",
    "plt.legend(loc = 4)\n",
    "ax.set_xlabel('log10 of C')\n",
    "ax.set_ylabel('Mean Val AUC')\n",
    "plt.title('X-validated AUC by C')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>We see that AUC is definitely affected by the choice of regularization strength (here we seem to do better with less regularization, probably due to very strong signal-to-noise in the data). But its hard to see what is best in the range $1$ to $10^{30}$. We can zoom in to see this better."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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CQQFl2D/P2P4HqOajkFjWoIz/yozt90E3Fi9HAXJ5WFbSmn/TqkoUlXgvChAL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\n3QeNhj0D+ACajKi39tFZaB7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      "text/plain": [
       "<matplotlib.figure.Figure at 0x109803d10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111)\n",
    "\n",
    "res2 = res[(res['e']>-6)]\n",
    "\n",
    "best = res2['mu'].max()\n",
    "best_1sde = best - res2['sig'][(res2['mu']==best)]/np.sqrt(10)\n",
    "\n",
    "plt.plot(res2['e'], res2['mu'], label='Avg AUC')\n",
    "plt.plot(res2['e'], res2['low'], 'k--', label='Low 95%')\n",
    "plt.plot(res2['e'], res2['up'], 'k--', label='Up 95%')\n",
    "plt.plot(res2['e'], best_1sde.values[0]*np.ones(res2.shape[0]), 'r', label='best_1sde')\n",
    "\n",
    "plt.legend(loc=4)\n",
    "ax.set_xlabel('log10 of C')\n",
    "ax.set_ylabel('Mean Val AUC')\n",
    "plt.title('X-validated AUC by C')\n",
    "\n",
    "e_max = res2['e'][(res2['mu']==best)].values[0]\n",
    "e_1sde = res2['e'][(res2['mu']>=best_1sde.values[0])].values.min()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>So now we have 2 ways to select our regularization:\n",
    "<ul>\n",
    "    <li>Choose C with $max(AUC_{xval})$</li>\n",
    "    <li>Choose min(C) where $AUC_{xval}^C>max(AUC_{xval})-stderr(max(AUC_{xval})$</li>\n",
    "</ul><br>\n",
    "This latter decision criteria is more conservative and accounts for the fact that we have variance in our cross-validated estimates of AUC. We argue that any $C$ where $AUC_{xval}^C>max(AUC_{xval})-stderr(max(AUC_{xval})$ is statistically equivalent to the max. Therefore we take the most conservative, least complex model option.<br><br>\n",
    "\n",
    "Now that we have selected a model, let's retrain on the full training set and evaluate on the test. We'll bootstrap the testing estimation so we can get a sense of the variance.\n",
    "</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def testAUCBoot(test, nruns, model, lab):\n",
    "    '''\n",
    "    Samples with replacement, runs multiple eval attempts\n",
    "    returns all bootstrapped results\n",
    "    '''\n",
    "    auc_res = []; oops = 0\n",
    "    for i in range(nruns):\n",
    "        test_samp = test.iloc[np.random.randint(0, len(test), size=len(test))]\n",
    "        try:\n",
    "            auc_res.append(roc_auc_score(test_samp[lab], model.predict_proba(test_samp.drop(lab,1))[:,1]))\n",
    "        except:\n",
    "            oops += 1\n",
    "    return auc_res"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "lab = 'y_buy'\n",
    "logreg_max = linear_model.LogisticRegression(C=10**e_max)\n",
    "logreg_max.fit(train.drop(lab,1),train[lab])\n",
    "auc_max = testAUCBoot(test, 100, logreg_max, lab)\n",
    "\n",
    "logreg_1sde = linear_model.LogisticRegression(C=10**e_1sde)\n",
    "logreg_1sde.fit(train.drop(lab,1),train[lab])\n",
    "auc_1sde = testAUCBoot(test, 1000, logreg_1sde, lab)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Now let's look at the distribution of AUC across the bootstrapped samples. Even though we can't use the test data for model selection, we can at least look at the test results for models built with the 2 selection criteria discussed above.\n",
    "\n",
    "</p>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x109d1a6d0>"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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6YMmSJQCgHNwf0tfXh7W1NUxMTAAAS5Ysweuvvw43Nzfk5eXB09MTP/74o7L8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\nREQKJgUiIlL8H4SItJma3XSWAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x108f34550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "r = [min(min(auc_max), min(auc_1sde)),max(max(auc_max), max(auc_1sde))]\n",
    "b = 15\n",
    "fig = plt.figure()\n",
    "frame = plt.gca()\n",
    "ax = fig.add_subplot(111)\n",
    "h1 = plt.hist(auc_max, range=r, bins=b, normed=True, histtype='step',stacked=True,label='max({})'.format(round(mean(auc_max),3)))\n",
    "h2 = plt.hist(auc_1sde,range=r, bins=b, normed=True, histtype='step',stacked=True,label='1sde({})'.format(round(mean(auc_1sde),3)))\n",
    "plt.legend()\n",
    "\n",
    "ax.set_xlabel('bootstrapped Test AUC')\n",
    "ax.set_ylabel('Pct Runs')\n",
    "plt.title('Distribution of BootStrap Test AUC')\n"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
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